• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.36 no.5
• /
• pp.438-447
• /
• 2008

This study is focused on reliability based design optimization (RBDO) using moving least squares. A response surface is used to derive a limit-state equation for reliability based design optimization. Response surface method (RSM) with least square method (LSM) or Kriging will be used as a response surface. RSM is fast to make the response surface. On the other hand, RSM has disadvantage to make the response surface of nonlinear equation. Kriging can make the response surface in nonlinear equation precisely but needs considerable amount of computations. The moving least square method (MLSM) is made of both methods (RSM with LSM+Kriging). Numerical results by MLSM are compared with those by LMS in Rosenbrock function and six-hump carmel back function. The RBDO of engine duct of smart UAV is pursued in this paper. It is proved that RBDO is useful tool for aerospace structural optimal design problems.

• Structural Engineering and Mechanics
• /
• v.76 no.6
• /
• pp.675-685
• /
• 2020

As the classical response surface method (RSM), the polynomial RSM is so easy-to-apply that it is widely used in reliability analysis. However, the trade-off of accuracy and efficiency is still a challenge and the "curse of dimension" usually confines RSM to low dimension systems. In this paper, based on the univariate decomposition, the polynomial RSM is executed in a new mode, called as DPRSM. The general form of DPRSM is given and its implementation is designed referring to the classical RSM firstly. Then, in order to balance the accuracy and efficiency of DPRSM, its adaptive order revision around the most probable point (MPP) is proposed by introducing the univariate polynomial order analysis, noted as RDPRSM, which can analyze the exact nonlinearity of the limit state surface in the region around MPP. For testing the proposed techniques, several numerical examples are studied in detail, and the results indicate that DPRSM with low order can obtain similar results to the classical RSM, DPRSM with high order can obtain more precision with a large efficiency loss; RDPRSM can perform a good balance between accuracy and efficiency and preserve the good robustness property meanwhile, especially for those problems with high nonlinearity and complex problems; the proposed methods can also give a good performance in the high-dimensional cases.

• Knowledge Management Research
• /
• v.20 no.3
• /
• pp.39-47
• /
• 2019

Response surface methodology (RSM) is a group of statistical modeling and optimization methods to improve the quality of design systematically in the quality engineering field. Its final goal is to identify the optimal setting of input variables optimizing a response. RSM is a kind of knowledge management tool since it studies a manufacturing or service process and extracts an important knowledge about it. In a real problem of RSM, it is a quite frequent situation that considers multiple responses simultaneously. To date, many approaches are proposed for solving (i.e., optimizing) a multi-response problem: process capability function approach, desirability function approach, loss function approach, and so on. The process capability function approach first estimates the mean and standard deviation models of each response. Then, it derives an individual process capability function for each response. The overall process capability function is obtained by aggregating the individual process capability function. The optimal setting is given by maximizing the overall process capability function. The existing process capability function methods usually use the arithmetic mean or geometric mean as an aggregation operator. However, these operators do not guarantee the Pareto optimality of their solution. Moreover, they may bring out an unacceptable result in terms of individual process capability function values. In this paper, we propose a maximin-based process capability function method which uses a maximin criterion as an aggregation operator. The proposed method is illustrated through a well-known multiresponse problem.

• Structural Engineering and Mechanics
• /
• v.49 no.1
• /
• pp.111-128
• /
• 2014

The stochastic response surface method (SRSM) and the response surface method (RSM) are often used for structural reliability analysis, especially for reliability problems with implicit performance functions. This paper aims to compare these two methods in terms of fitting the performance function, accuracy and efficiency in estimating probability of failure as well as statistical moments of system output response. The computational procedures of two response surface methods are briefly introduced first. Then their capabilities are demonstrated and compared in detail through two examples. The results indicate that the probability of failure mainly reflects the accuracy of the response surface function (RSF) fitting the performance function in the vicinity of the design point, while the statistical moments of system output response reflect the accuracy of the RSF fitting the performance function in the entire space. In addition, the performance function can be well fitted by the SRSM with an optimal order polynomial chaos expansion both in the entire physical and in the independent standard normal spaces. However, it can be only well fitted by the RSM in the vicinity of the design point. For reliability problems involving random variables with approximate normal distributions, such as normal, lognormal, and Gumbel Max distributions, both the probability of failure and statistical moments of system output response can be accurately estimated by the SRSM, whereas the RSM can only produce the probability of failure with a reasonable accuracy.

• Proceedings of the KSME Conference
• /
• 2001.06c
• /
• pp.580-585
• /
• 2001

A response surface method(RSM) is utilized for structural optimization and implemented on a parametric CAD platform. Once an approximation of the performance function is made, no formal design sensitivity analysis is necessary. The approximation gives the designer the sensitivity information and furthermore intuition on the performance functions. The scheme for the design of experiment chosen for the RSM has a large influence on the accuracy of converged solutions and the amount of computation. The D-optimal design criterion as implemented in this paper is found efficient for the structural optimization. The program is developed on a parametric CAD platform and tested using several shape design problems of such as a torque arm and a belt clip. It is observed that the RSM used provides a faster convergence than other approximation methods for design sensitivity.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.9 no.2
• /
• pp.116-129
• /
• 2001

Traditional occupant analysis has been performed with a pre-determined crash puse which is produced from a test and the involved components are designed based on the analysis resuls. The method has limitations in that the design does not have much freedom. Howrver, if a good crash pulse is proposed, the body structure can be modified to generate the crash pulse. Therefore, it is assumed that the crash pulse can be changed to imptove the occupant crash performance. A preferable crash pulse is determined to minimize the occupant injuty. A constraint is established to keep the phenomena of physics valid. The response surface method(RSM) is adopted for the optimization process. An RSM in a commercial code is utilzed by interfacing with an in-house occupant analysis program called SAFE(Safety Analysis For occupant crash Enviroment). Design of involved components called is carried out through optimization with the RSM. The advantages of the RSM are investigated as opposed to other methods, and the tesults are compared. Also, the design under the new crach pulse is compared with that trom the pre-detetmined pulse.

• Integrative Medicine Research
• /
• v.6 no.4
• /
• pp.388-394
• /
• 2017

Background: The present study optimized ultrasound-assisted extraction conditions to maximize extraction yields of glycyrrhizic acid from licorice. Methods: The optimal extraction temperature ($X_1$), extraction time ($X_2$), and methanol concentration ($X_3$) were identified using response surface methodology (RSM). A central composite design (CCD) was used for experimental design and analysis of the results to obtain the optimal processing parameters. Results: Statistical analyses revealed that three variables and the quadratic of $X_1$, $X_2$, and $X_3$ had significant effects on the yields and were followed by significant interaction effects between the variables of $X_2$ and $X_3$ (p<0.01). A 3D response surface plot and contour plots derived from the mathematical models were applied to determine the optimal conditions. The optimum ultrasound-assisted extraction conditions were as follows: extraction temperature, $69^{\circ}C$; extraction time, 34?min; and methanol concentration, 57%. Under these conditions, the experimental yield of glycyrrhizic acid was 3.414%, which agreed closely with the predicted value (3.406%). Conclusion: The experimental values agreed with those predicted by RSM models, thus indicating the suitability of the model employed and the success of RSM in optimizing the extraction conditions.

• Journal of Advanced Marine Engineering and Technology
• /
• v.31 no.1
• /
• pp.58-66
• /
• 2007

Genetic Algorithms (GA) have some difficulties in practical applications because of too many function evaluations. To overcome these limitations, an approximated modeling method such as Response Surface Modeling(RSM) is coupled to GAs. Original RSM method predicts linear or convex problems well but it is not good for highly nonlinear problems cause of the average effect of the least square method(LSM). So the locally approximated methods. so called as moving least squares method(MLSM) have been used to reduce the error of LSM. In this study, the efficient evolutionary GAs tightly coupled with RSM with MLSM are constructed and then a 2-dimensional inviscid airfoil shape optimization is performed to show its efficiency.

• Journal of Korean Society on Water Environment
• /
• v.25 no.6
• /
• pp.943-950
• /
• 2009

Cadmium (Cd) adsorption onto the activated carbon containing hydroxyapatite (HAP) was investigated in batch experiments and response surface methodology (RSM) using the Box-Behnken methods were applied to the experimental results. Cd adsorption with different HAP mass ratio of from 10% to 30%. With more HAP, Cd was more adsorbed. These results suggest that the higher HAP mass causes an increase of the ion exchange potential of the HAP sorbent. Equilibrium experimental results from Cd adsorption was fitted to Langmuir and Freundlich isotherm models. Cd adsorption on HAP sorbent were found to follow the Freundlich isotherm model well in the initial adsorbate concentration range. Also, Cd adsorption was a function of the HAP mass ratio ($x_1$), initial Cd concentration ($x_2$), and initial pH ($x_3$) from the application of the RSM. Statistical results showed the order of significance of the independent variables to be initial Cd concentration > HAP mass ratio > initial pH.

• Proceedings of the KIEE Conference
• /
• summer
• /
• pp.1097-1099
• /
• 2004

This paper deals with the optimal design of a slotless type of permanent magnet linear synchronous motor (PMLSM). Response surface methodology, one of the optimization methods, is used to consider multiple response of the PMLSM. That is, it is applied to obtain more average thrust and less thrust ripple than prototype PMLSM. To analyze quickly, characteristic analysis of the PMLSM is performed by space harmonic method and final results of optimized PMLSM are compare with those of prototype PMLSM through finite element analysis.